Answer:
The number of complete award announcements possible are 19,554,575,040.
Step-by-step explanation:
Combination is the number of ways to select <em>k</em> items from <em>n</em> distinct items when the order of selection does not matters.
Whereas permutation is the number of ways to select <em>k</em> item from <em>n</em> items when order of selection matters.
The number of people entering this year is 22.
The number of ways to select 5 people for Grand Prize is,
.
The remaining number of people is, 22 - 5 = 17.
It is provided that the other 5 are selected according to an order.
The number of ways to select other 5 winners is,
![^{17}P_{5}=\frac{17!}{(17-5)!} =742560](https://tex.z-dn.net/?f=%5E%7B17%7DP_%7B5%7D%3D%5Cfrac%7B17%21%7D%7B%2817-5%29%21%7D%20%3D742560)
The total number of ways to select 10 winners of 22 is:
Total number of ways = 26334 × 742560 = 19,554,575,040.